Problem: Add 53.463 to 12.9873 and round to the nearest thousandth.
Solution: We first add the two numbers: \begin{align*} 53.463+ 12.9873 &= 66.4503 \end{align*}In order to round to the nearest thousandth, we must look at the ten-thousandths digit, which here is 3. Because 3 is less than or equal to 4, the thousandths place remains 0. So, rounding 66.450 to the nearest thousandth yields $\boxed{66.450}$.